Question: Simplify the following expression: $\dfrac{a^4}{10a^2}$ You can assume $a \neq 0$.
$ \dfrac{a^4}{10a^2} = \dfrac{1}{10} \cdot \dfrac{a^4}{a^2} $ To simplify $\frac{1}{10}$ , find the greatest common factor (GCD) of $1$ and $10$ $1 = $ $10 = 2 \cdot 5$ $ \mbox{GCD}(1, 10) = = 1 $ $ \dfrac{1}{10} \cdot \dfrac{a^4}{a^2} = \dfrac{1 \cdot 1}{1 \cdot 10} \cdot \dfrac{a^4}{a^2} $ $\phantom{ \dfrac{1}{10} \cdot \dfrac{4}{2}} = \dfrac{1}{10} \cdot \dfrac{a^4}{a^2} $ $ \dfrac{a^4}{a^2} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a} = a^2 $ $ \dfrac{1}{10} \cdot a^2 = \dfrac{a^2}{10} $